A process can be monitored for the purpose of detecting and eliminating special causes or for the purpose of adjusting the process to a target value. SPC (Statistical Process Control) methods are used for the purpose of locating and removing any unexpected changes in the quality characteristic. On the other hand, certain processes (manufacturing, chemical etc.) are monitored using APC (Automatic Process Control) methods which compensate for process variability and maintain the process as close as possible to a desired target value. The efficiency of control schemes can be increased by allowing the interval between the samples from the process to vary as a function of the process data. The following are developed for a process control problem using a variable sampling scheme: a model for the process mean, a performance criterion and an estimation technique. The process mean is a random walk model with a control variable. An observation for the process is the mean plus a random error. The Kalman filter estimation technique is used to estimate the time-varying process mean parameter of the process control problem. The objective is to determine the adjustment and sampling strategies that lead to a minimum expected loss. These adjustment and sampling limits address two questions namely, when to adjust and when to take the next sample. The performance of the VSI scheme is compared to the performance of the FSI scheme in terms of the percentage reduction in cost. Also, the effects of the cost combinations and the observation errors on the VSI and FSI are studied. / Ph. D.